# Tag: knowledge

## 3,700-Year-Old Babylonian Tablet Decoded

Almost a century ago, Edgar Banks – the inspiration for Indiana Jones – dug up a clay tablet in southern Iraq, but it took until now for its meaning to be understood. With this explanation has come insight into Babylonian mathematics, which operated on a different, and in some ways preferable, system than our own.

In 1945, it was realized that the tablet, known as Plimpton 322 after it was sold to collector George Plimpton for \$10, had mathematical significance, but the details remained a mystery. New research argues it represents part of a trigonometric table, and one more accurate than those that came afterwards.

Plimpton 322’s burial location in what was once the city of Larsa indicates it’s 3,700 years old, dating from the time of Hammurabi, who established one the earliest surviving legal codes. “Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realized it contains a special pattern of numbers called Pythagorean triples,” said Dr Daniel Mansfield of the University of New South Wales in a statement. Pythagorean triples are any whole numbers a, b, and c that can form a right-angle triangle through the formula a2 + b2 = c2, with 3, 4, and 5 being the most familiar example.

“The huge mystery, until now, was its purpose – why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet,” Mansfield continued.

Mansfield became interested in the problem and collaborated with his colleague Dr Norman Wildberger to try to unravel it. Wildberger is the inventor of a new way of doing trigonometry, based on the ratio of sides rather than angles. In 2005, he published a book, Divine Proportions: Rational Trigonometry to Universal Geometry, demonstrating that any problem that can be solved using traditional trigonometric methods canalso  be solved using his technique, and often more easily for those who have taken the time to learn it.

The idea of Plimpton 322 as a trigonometric table had been raised before, and eventually rejected, but this was done in the absence of an understanding of Wildberger’s methods.

Mansfield and Wildberger concluded that the ancient Babylonians had beaten Wildberger to his ideas by almost four millenia, albeit only for right-angled triangles. They report in Historica Mathematica that instead of using sinΘ, cosΘ, and tanΘ as we do – something we inherited from the ancient Greeks – Plimpton 322 could be used by anyone needing to know the length of one side of a right-angled triangle by finding the closest match to the two known sides.

“Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles,” Mansfield said. “It is a fascinating mathematical work that demonstrates undoubted genius.” The tablet would have been useful to architects or surveyors.

At some point since its making, a section of Plimpton 322 broke off. What remains are the side lengths for 15 right-angle triangles, ordered by inclination. Mansfield and Widlberger believe there were once 38 rows and 6 columns, making a truly impressive store of possible triangles.

The use of ratios in combination with the Babylonian base sixty number system, from which we get the length of our hours and minutes, made for an arguably superior method for calculating trigonometry to the table of chords created by the Greek mathematician Hipparchus more than 1,000 years later.

Mansfield told IFLScience that we have no idea why Babylonian trigonometry was lost. While it is possible that ancient mathematicians decided Hipparchus’ work was superior, it is also possible that Larsa and other centers of this knowledge lost a war, taking valuable knowledge with it. Mansfield noted that there is a gap in our records of the Babylonian civilization lasting several centuries.

When artifacts appear again, what we find comes mixed with influences from other cultures. Still, many Babylonian tablets have yet to be examined in detail, even aside from those that have yet to be dug up, so there may be plenty more we can learn about  Babylonian mathematics now that we have a hint.

For all the merits of Wildberger’s system, it has struggled to gain a foothold among mathematicians and teachers well versed in classical trigonometry. However, Mansfield speculates that Plimpton 322 might change this. The use of ratios rather than angles could become a matter of great interest to historians of mathematics, who may learn more about how it was done. Eventually, it may be taught in schools to show there is more than one way to think about trigonometry.

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Thousands of teenagers across England, Wales and Northern Ireland are receiving their A-and AS-level results. But, in England, there have been changes to this year’s A-level qualifications – the BBC News website sets out the changes.

Under the new system, students sit all A-level exams at the end of two years of study, instead of taking modular exams throughout the course.

AS-level results no longer count towards A-level grades. No subject will have more than a 20% coursework component and most courses will be assessed entirely through exams.

Resits will still be available, but January exams will be scrapped, so students will have to wait until May/June of the following year for a chance to improve their grades.

The change was brought in by the former Education Secretary Michael Gove with the intention of making the exams more “fit for purpose” – or harder.

The new AS- and A-levels syllabuses have been phased in across schools in England from September 2015.

The DfE says: “The content for the new A-levels has been reviewed and updated. Universities played a greater role in this for the new qualifications than they did previously.”

## What is happening to AS-levels?

The AS-level is being decoupled from the A-level, which means it operates as a stand-alone qualification and the results do not count towards A-level grades – although in Wales and Northern Ireland, they will still count towards an overall A-level mark.

Provisional figures from the Department for Education show that the number of entries for AS subjects has fallen by 42% this summer.

Association of School and College Leaders general secretary Geoff Barton said it “sounded the death knell for AS-levels”.

“The great benefit of the old system was that it gave students a broader range of knowledge and allowed them to keep their options open for longer,” he said.

“The decision to decouple these qualifications was an entirely unnecessary reform, which is narrowing the curriculum and reducing student choice.”

## Which subjects are being phased in when?

This year, new A-level qualifications were taken in:

• art and design
• biology
• chemistry
• computer science
• economics
• English language
• English language and literature
• English literature
• history
• physics
• psychology
• sociology

Next summer, candidates will sit the new A-level qualifications in the following subjects:

ancient languages (classical Greek, Latin)

• dance
• drama and theatre
• geography
• modern foreign languages (French, German, Spanish)
• music
• physical education
• religious studies

In the summer of 2019, new exams will be sat in:

• accounting
• ancient history
• ancient languages (biblical Hebrew A-level only)
• classical civilisation
• design and technology
• electronics
• environmental science
• film studies
• further mathematics
• geology
• government and politics
• history of art (A-level only)
• law
• mathematics
• media studies
• modern foreign languages (Arabic, Bengali, Gujarati, Greek, Japanese, modern Hebrew, Panjabi, Persian, Polish, Portuguese, Turkish, Urdu)
• modern foreign languages (Chinese, Italian, Russian)
• music technology
• philosophy
• statistics

## Hasn’t all this change been stressful for the teenagers involved?

Young people and teachers have told the BBC that preparing for the new qualification has been stressful, especially as there were no past papers to refer to and some text books were written before some of the syllabuses were finalised.

Rosamund McNeil, from the National Union of Teachers, said: “The upheaval of a hastily reformed curriculum and the changes leading to a reduction in much of the coursework elements, created unnecessary stress and concern for pupils and teachers alike.

“While results nationally may have remained in line with those in the previous year, some schools and colleges will no doubt see considerable variation.

“The volatility around results and the accountability measures which use them can have damaging and unfair consequences.”

## What is happening elsewhere in the UK?

There have been no major changes in the other nations.

In Wales and Northern Ireland, AS-levels have remained as an integral part of studying for A-levels.

AS-levels contribute 40% of the total marks of the full A-level and can be taken at the end of the AS course or alongside A2.

In Scotland, students do not sit A-levels and AS-levels. Instead, they take Highers and Advanced Highers.

This year, the Higher pass rate dipped by 0.2%, but the total number of passes remained above 150,000 for a third successive year.

Reporting by BBC News education reporter Katherine Sellgren

## Related Topics

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## Our Obsession With Smartphones Reduces Our Brain Power, Says Study

Younger generations are often accused of going around glued to their phones (although the rise of the silver surfer means this isnt strictly fair). Even though you can argue that means infinite knowledge and information at your fingertips, a new study has shownsmartphones can also reduce our brain power and a specifictype of intelligence.

Its all down to our attention continuously wandering towards our phones, which the researchers argue in their study published in the online Journal of the Association of Consumer Researchis reducing our available cognitive capacity.

They decided to test the brain drain hypothesis, which posits that knowing our smartphone is in the vicinity uses up limited-capacity cognitive resources, thereby leaving fewer resources available for other tasks and undercutting cognitive performance.

The brain has a finite pool of attention resources the limited-capacity cognitive resources that control both attention and other cognitive processes. When these resources are used to try and prevent automatic attention going towards our phone, we are tying up these resources, making them unavailable to carry out other tasks, meaning the performance of these tasks suffer.

The researchers discovered that just by having a smartphone in your eye line, you are more likely to fail at simple tasks and remembering things, and this holds true when your phone is in your pocket, your bag, or even in the next room.

To studythis, they conducted experiments testing 520 university students on their memory and intelligence while in the presence of their phones. The participants answered exam questions that tested mathematics, memory, and reasoning, while their phones were randomly assigned to be on their desk, in their pocket, in their bag, or in the next room.

The results showed that those who kept their phone on their desk (in eyesight) scored 10 percent lower on questions that testedfocus and memory. They also reacted slower to speed tests. In fact, even when their phones were turned off or on do not disturb mode, if they were on the desk, the participant scored lower than those whose phones were in the next room.

This means smartphones diminish a person’s working memory capacity and “fluid intelligence” the ability to solve novel problems independent of already stored information, which is calledcrystallized intelligence.

Unsurprisingly, they found that the negative effects of having your phone nearby was greater for those who self-identified as being dependent on their phones. They think this effect is not because the smartphone users mind is being distracted by thoughts of checking for messages, but rather their mind is concentrating on trying not to be distracted, at the expense of the performance of the task at hand.

“Your conscious mind isn’t thinking about your smartphone, but that process the process of requiring yourself not to think about something uses up some of your limited cognitive resources, concluded lead author Dr Adrian Ward in a statement. It’s a brain drain.”

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## Even An AI Supercomputer Found This College Entrance Exam Tough

If you are getting stressed about upcoming exams then youre not alone, so is this artificially intelligent (AI) machine.

Last week, a top AI system was pitted against nearly 10 million students to face the maths paper for a much-feared Chinese university entrance exam, known as gaokao. Unfortunately for robotkind, its results were pretty mediocre.

The computer a humming tower of eleven servers with no Internet connection called AI-MATHS scored 105 points out of 150 points. On another version of the test, it scored 100. Although that beats the passing score of 90, humanities students had previously scored an average of 109 last year.

That said, the machine finished the exam in 10 minutes when humans are given two hours to complete the exam.

Scientists recently saidartificial intelligence will be able to beat humans at everything by 2060, whether that’squizzes, exams, chess, or the game Go. In response to the study, Elon Musk then tweeted that he believes AI-superiority will actually be earlier, around 2030 or 2040.

That doesnt mean this AI is slow off the mark, however. The computer itself would be able to deal with raw numbers with no problem. Instead, the purpose of this task was to understand the examination in terms of language, something that computers are not so sharp with at the moment.

“This is not a make-or-break test for a robot. The aim is to train artificial intelligence to learn the way humans reason and deal with numbers,” said Lin Hui, CEO of Chengdu Zhunxingyunxue Technology, who developed the AI, according to Chinese news agencyXinhua.

For example, the robot had a hard time understanding the words ‘students’ and ‘teachers’ on the test and failed to understand the question, so it scored zero for that question.

Gaokao isinfamously rigorous and renowned for being overwhelming stressful for the young people that take it. Made up of four three-hour papers in Chinese, English, mathematics, and a choice of either sciences or humanities, the series of tests rely on an extensive range of knowledge, problem-solving skills, and obscure creative thinking. The mathematics exam itself is said to be about as tough as the same level college exam in the West.

Nevertheless, the researchers continue to work with China’s Ministry of Science and Technology and remain optimistic their AI will improve in the exams in no time at all.

I hope next year the machine can improve its performance on logical reasoning and computer algorithms and score over 130,” Lin added.

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## Knowing Names Makes Cooperation More Likely

Names are powerful things. Just knowing what someone calls themself makes us more likely to cooperate rather than compete with them, a new study has found. The discovery could prove useful in reducing conflict, but some writers of fiction might be asking scientists what took you so long?

Social scientists have spent much effort testing variations of the Prisoner’s Dilemma to find out under what circumstances people prefer to cooperate for the common good, rather than seek their own advantage. It’s hardly surprising that people are more likely to cooperate with those they already trust or are likely to interact with in the future. However, according to Zhen Wang and co-authors, even the tiny connection provided by knowing another participant’s name increases the chanceof cooperation.

Wang of the Northwestern Polytechnical University in China collaborated with researchers from five other countries on the project. They studied the behavior of 154 randomly paired Yunnan University undergraduates who interacted in repeated Prisoner’s Dilemma scenarios, where they had the choice to cooperate, defect, or punish the other player, with the knowledge they would probably have future rounds with the same partner.

Cooperators sacrificed one unit so the other player got two. Defectors got a unit for themselves at the expense of the other player, while those who optedfor punishment lost one unit while penalizing the other player four units, discouraging past defectors from repeating their actions.

In Science Advances, Wang reports that knowing each others’ names was enough to induce most participants to cooperate initially, in contrast to anonymous rounds where defection dominated.

The authors acknowledge the possibility the result was enhanced by the participants being classmates of similar background. Nevertheless, the effect was large compared to those seen from other attempts to tweak Prisoner’s Dilemma outcomes.

The Prisoner’s Dilemma has been intensively studied partly because human survival depends on cooperation, so finding ways to increase it has value. This work has been further spurred by the observation that cooperation is common in nature, in defiance of crude evolutionary models, which predicted it should seldom exist. The drive to understand the discrepancy has greatly expanded what we know about the workings of evolution, including studies of the way that cooperators, by grouping together, can offset the advantagegained by free riders who profit from others’ generosity while offering none of their own.

Although this may be the first scientific proof, the idea we care more for those whose names we know is widespread. Our names shape how people treat us, possibly enough to change how we look. In The West Wingseries, Leo McGarry complained he couldn’t eat the lobsters his daughter had named, a phenomenon common enough for the audience to recognize.

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## Scientists Discover 40 New Genes Linked To Intelligence

As the great debate over nurture versus nature continues, a team of geneticists have identified 40 new genes that have a direct influence over human intelligence. Writing in the journal Nature Genetics, the team conclude that there are now at least 52 genes that have a direct influence on a persons IQ.

Analyzing the genomes of 60,000 adults and 20,000 children, the team led by the Free University of Amsterdam found that these 40 new genes guide the construction of healthy neurons, as well as the synapse connections that branch between them.

Its likely that there are hundreds of additional genes that have an influence over IQ, so although this study represents the biggest haul yet in this regard, theres still a long way to go before the cartography of our cognitive abilities is complete.

The team note that these 40 new genes, when all other factors are ruled out, explain just 4.8 percent of the variation in human intelligence seen over their subjects. If 50 percent of a persons IQ can be explained genetically, then this means that there is a huge chasm of knowledge that geneticists have yet to fill.

These findings provide starting points for understanding the molecular neurobiological mechanisms underlying intelligence, one of the most investigated traits in humans, the authors write in their study.

Just to clarify straight off the bat these genes have an influence on intelligence, but environmental factors, including lifestyle, healthcare, socio-economic background, education, and so on also have a huge effect.

Furthermore, IQ tests two types of cognitive facets known as crystallized intelligence and fluid intelligence.

The former is the ability of a person to solve puzzles or answer questions when the parameters of the problem have already been understood or conveyed clearly mathematics is a good example of this. Fluid intelligence is the ability to solve brand new and more abstract problems, like navigating a maze, spotting hidden patterns, or even weaving through a conversation with a complete stranger.

There are plenty of other types of intelligence, including emotional intelligence the ability to empathize, to regulate ones own emotions, and to handle interpersonal relationships well. IQ does not take this into account, and neither do these 52 genes.

This study also only looked at the genomes of those with European descent. Other research groups will have to peer into the genetic makeup of those from other geographical settings to see if the same genes are present all over the world.

In any case, this is a remarkable study that represents a giant leap forward in our understanding of what has been referred to as the architecture of intelligence. Its a tall mountain to climb, but another ledge has just been scaled by this research team.

[H/T: Guardian]

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## The Map Of Mathematics

If you want to up your nerd-level, just watch this video by Dominic Walliman about the different fields of math. But beware: Over 350,000 people already have seen this and might be a lot smarter by now. Try to keep up!

“The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.”

via: sploid

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